Chapter 12.5, Problem 15PPS

To determine

To state whether the events are mutually exclusive or not mutually exclusive and find the probability.

Answer to Problem 15PPS

The events are mutually exclusive and the probability that she will bowl either a spare or a strike for any given frame is $\frac{3}{4}\text{ or 75\%}$ .

Explanation of Solution

Given information:

The given statement is:

“Cindy’s bowling records indicate that for any frame, the probability that she will bowl a strike is $30\%$ , a spare $45\%$ and neither $25\%$ . What is the probability that she will bowl either a spare or a strike for any given frame?”

Formula used:

The following formula is used:

  $\text{Probability}=\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}$

Calculation :

The events are mutually exclusive because a she cannot bowl both a spare and a strike for a given frame.

The probability can be calculated by;

  $\begin{array}{l}\text{P}\left(\text{spare}\right)=\frac{45}{100}\\ \text{P}\left(\text{strike}\right)=\frac{30}{100}\\ \text{P}\left(\text{spare or strike}\right)=\frac{45}{100}+\frac{30}{100}\\ \text{P}\left(\text{spare or strike}\right)=\frac{75}{100}\\ \text{P}\left(\text{spare or strike}\right)=\frac{3}{4}\text{ or 75\%}\end{array}$

Hence, the events are mutually exclusive and the probability that she will bowl either a spare or a strike for any given frame is $\frac{3}{4}\text{ or 75\%}$ .